Subject: Isn't the twins paradox a paradox?

The TWINS PARADOX is often cited as an example of what happens to time when 
acceleration or gravity effect participants.  Twin A takes a trip, 
accelerating to significant speeds, and returns to find he has a different age 
than Twin B.

I do not question the relative nature of time;  there is a significant body of 
experimental evidence to substantiate the theory.  But I have a problem with 
this example.  It seems to me that, for Twin A to return to Twin B, it is 
required that he DECELERATE and reverse his motion. Put another way, when Twin 
A decelerates, it is the same thing as Twin B accelerating;  their relative 
time flows are reversed.

Thus, in my understanding, whenever two twins (or other objects) are removed 
from each others frame of reference, TO AN INDEPENDENT OBSERVER, their 
timerates might be different.  But in order to bring these two back into 
exactly the same of reference requires an exactly opposite motion, which 
should cancel out with the original.  I don’t see how they would thus have 
different ages, although I completely understand that they would perhaps have 
different ages all the time they are apart.

Let me try it one more way.  Suppose instead of Twin A returning, Twin B later 
joins Twin A at Alpha Centuri.  Wouldn’t they then have the same age?  
Wouldn’t they always have the same age as whenever they returned to the same 
frame of reference, with all intervening time distortions due to movement 
canceling out?

Am I missing something?

Re: Isn't the twins paradox a paradox?